Finite Group Databasebeta

← Group #481458

Character table — Group #481458

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444222222444444222244444444444444448888888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1
χ9111111111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-111-1-1
χ10111111111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111
χ11111111111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11-1-111
χ12111111111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-1
χ13111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-111
χ14111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-1
χ15111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-1
χ16111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1-1-111
χ171111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-11-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-1-111-11-1
χ181111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-11-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-111-1-11-11
χ191111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-11-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-111-1-11-11
χ201111-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-11-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-1-111-11-1
χ211111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1111-1-11-11-11
χ221111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-111-11-11-1
χ231111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-1-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-111-11-11-1
χ241111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-11-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-11-1-11-11-11
χ251111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11
χ261111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-111-1
χ271111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-1-1-111111-1-11-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111-111-1
χ281111-1-1-1-11-1-1-1-11-1-1111111-1-111-1-1-1-1-1-111111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-11-1-11
χ291111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1111111-1-1-1-11-1-11ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-111-1
χ301111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1111111-1-1-1-11-1-11ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1-1111-1-11
χ311111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1111111-1-1-1-11-1-11−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1-1111-1-11
χ321111-1-1-1-11-1-1-1-11-1-11111-1-111-1-1111111-1-1-1-11-1-11−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-111-1
χ33222222222222222222222222-2-2-2-2-2-2222-2-22-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2222222-2-2-222-2-2-2-2-20000000000000000000000000000000000000000
χ35222222222-2-2-2-2222-2-2-2-222-2-2-2-2-2-22222-222-2-2-2220000000000000000000000000000000000000000
χ36222222222-2-2-2-2222-2-2-2-2-2-2222222-2-2-2-22-2-22-2-2220000000000000000000000000000000000000000
χ372222-2-2-2-2222222-2-2-2-2-2-22222-2-222-2-2-2-2-222-2-22-220000000000000000000000000000000000000000
χ382222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-222222-2-22-22-220000000000000000000000000000000000000000
χ392222-2-2-2-22-2-2-2-22-2-2222222-2-2-2-22222-2-22-2-22-222-20000000000000000000000000000000000000000
χ402222-2-2-2-22-2-2-2-22-2-22222-2-22222-2-2-2-222-222-2-222-20000000000000000000000000000000000000000
χ412-2-2222-2-2222-2-2-22-222-2-200002i−2i2i−2i2i−2i0002i−2i0000000000000000000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00000000
χ422-2-2222-2-2222-2-2-22-222-2-200002i−2i2i−2i2i−2i0002i−2i000000000000000000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00000000
χ432-2-2222-2-2222-2-2-22-222-2-20000−2i2i−2i2i−2i2i000−2i2i0000000000000000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00000000
χ442-2-2222-2-2222-2-2-22-222-2-20000−2i2i−2i2i−2i2i000−2i2i000000000000000000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00000000
χ452-2-2222-2-22-2-222-22-2-2-22200002i−2i2i−2i−2i2i000−2i2i0000000000000000000001−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00000000
χ462-2-2222-2-22-2-222-22-2-2-22200002i−2i2i−2i−2i2i000−2i2i000000000000000000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00000000
χ472-2-2222-2-22-2-222-22-2-2-2220000−2i2i−2i2i2i−2i0002i−2i0000000000000000000001+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000
χ482-2-2222-2-22-2-222-22-2-2-2220000−2i2i−2i2i2i−2i0002i−2i000000000000000000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000
χ492-2-2222-2-2-22-22-22-222-22-22-22-20000002-2200-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ502-2-2222-2-2-22-22-22-222-22-22-22-20000002-2200-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ512-2-2222-2-2-22-22-22-222-22-2-22-22000000-22-200200002−22−22−22−2−22−22−22−22000000000000000000000000
χ522-2-2222-2-2-22-22-22-222-22-2-22-22000000-22-20020000−22−22−22−222−22−22−22−2000000000000000000000000
χ532-2-2222-2-2-2-22-222-22-22-222-2-220000002-2-200200002−22−2−22−222−22−2−22−22000000000000000000000000
χ542-2-2222-2-2-2-22-222-22-22-222-2-220000002-2-20020000−22−222−22−2−22−222−22−2000000000000000000000000
χ552-2-2222-2-2-2-22-222-22-22-22-222-2000000-22200-20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ562-2-2222-2-2-2-22-222-22-22-22-222-2000000-22200-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ572-2-22-2-222222-2-2-2-22-2-22200002i−2i−2i2i2i−2i000−2i2i0000000000000000000001−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i00000000
χ582-2-22-2-222222-2-2-2-22-2-22200002i−2i−2i2i2i−2i000−2i2i000000000000000000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i00000000
χ592-2-22-2-222222-2-2-2-22-2-2220000−2i2i2i−2i−2i2i0002i−2i0000000000000000000001+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i00000000
χ602-2-22-2-222222-2-2-2-22-2-2220000−2i2i2i−2i−2i2i0002i−2i000000000000000000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i00000000
χ612-2-22-2-2222-2-222-2-2222-2-200002i−2i−2i2i−2i2i0002i−2i0000000000000000000001+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i00000000
χ622-2-22-2-2222-2-222-2-2222-2-200002i−2i−2i2i−2i2i0002i−2i000000000000000000000−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i00000000
χ632-2-22-2-2222-2-222-2-2222-2-20000−2i2i2i−2i2i−2i000−2i2i0000000000000000000001−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i00000000
χ642-2-22-2-2222-2-222-2-2222-2-20000−2i2i2i−2i2i−2i000−2i2i000000000000000000000−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i00000000
χ652-2-22-2-222-22-22-222-2-22-222-22-2000000-22-200200002−2−222−2−222−2−222−2−22000000000000000000000000
χ662-2-22-2-222-22-22-222-2-22-222-22-2000000-22-20020000−222−2−222−2−222−2−222−2000000000000000000000000
χ672-2-22-2-222-22-22-222-2-22-22-22-220000002-2200-20000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ682-2-22-2-222-22-22-222-2-22-22-22-220000002-2200-20000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ692-2-22-2-222-2-22-2222-22-22-22-2-22000000-22200-20000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000000000000000
χ702-2-22-2-222-2-22-2222-22-22-22-2-22000000-22200-20000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000000000000000
χ712-2-22-2-222-2-22-2222-22-22-2-222-20000002-2-200200002−2−22−222−2−222−22−2−22000000000000000000000000
χ722-2-22-2-222-2-22-2222-22-22-2-222-20000002-2-20020000−222−22−2−222−2−22−222−2000000000000000000000000
χ7344444444-44-4-44-4-4-44-4-44000000000000000000000000000000000000000000000000000000000000
χ7444444444-4-444-4-4-4-4-444-4000000000000000000000000000000000000000000000000000000000000
χ754444-4-4-4-4-44-4-44-444-444-4000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-4-4-444-4-4444-4-44000000000000000000000000000000000000000000000000000000000000
χ7788-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ798-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).